Our method reduces the solution of problem to the solution of a system ofalgebraic equations and the approximate solution is obtained in terms of Taylor polynomials.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study we consider a third order linear differential equation with variable coefficients characterizingspherical curves according to Frenet frame in Euclidean 4-Space E 4 .
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Key Findings & Data:This equation whose coefficients arerelated to special function, curvature and torsion, is satisfied by the position vector of any regular unitvelocity spherical curve.
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Conclusion & Impact:Our method reduces the solution of problem to the solution of a system ofalgebraic equations and the approximate solution is obtained in terms of Taylor polynomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this study we consider a third order linear differential equation with variable coefficients characterizingspherical curves according to Frenet frame in Euclidean 4-Space E 4 . This equation whose coefficients arerelated to special function, curvature and torsion, is satisfied by the position vector of any regular unitvelocity spherical curve. These type equations are generally impossible to solve analytically and so, forapproximate solution we present a numerical method based on Taylor polynomials and collocations pointsby using initial conditions. Our method reduces the solution of problem to the solution of a system ofalgebraic equations and the approximate solution is obtained in terms of Taylor polynomials.
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Cite This Article
AYDIN, T. A., SEZER, M. (2022). Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 15 - Sayı: 1, 1–7. https://ajindex.com/articles/472207
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